Solving Word Problems - Sine/Cosine Functions PDF

11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d Student: How to Solve a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c)+d or f(x) = a\sin(bx+c)+d https://study.com/skill/learn/h...

11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d Student: How to Solve a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c)+d or f(x) = a\sin(bx+c)+d https://study.com/skill/learn/how-to-solve-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cosbx-plus-c-plus-d-or-f-x-a-sin-bx-plus-c-plus-d-explanation.html 1. A quantity y is a periodic function of time t, with the relationship between y and t having the form y(t) = a sin(bt + c) + d, t ≥ 0. If the periodic changes in the values of y(t) have a mean level of 10, an amplitude of 5, a period of π, and a phase constant of 3, find the function y(t).  y(t) = 5 sin(2t + 3) − 10 y(t) = 5 sin(2t − 3) + 10 y(t) = 5 sin(πt + 3) + 10 y(t) = 5 sin(πt − 3) − 10 2. A quantity y is a periodic function of time t, with the relationship between y and t having the form y(t) = a sin(bt + c) + d, t ≥ 0. If the periodic changes in the values of y(t) have a mean level of 10, an amplitude of 5, a period of π, and a phase constant of 3. What is the maximum value of y. -5  0 15 5 3. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) + 7. What is the period of this motion? 1/2 2  4π 4 https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 1/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 4. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) + 7. What is the mean level of this oscillatory motion?  7 -6 -7 4 5. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) + 7. What is the phase constant?  -6 4π 7 6 6. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) + 7. What is the amplitude?  4 7 -6 4π 7. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) + 7. What is angular velocity?  4π -6 4 7 8. A particle is performing an oscillatory motion and follows the equation y = 4 sin(4πt − 6) − 7. What is the mean level of this oscillatory motion? -4 7  -7 4 https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 2/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 9. A particle is performing an oscillatory motion and follows the equation y = 10 cos(10πt − 10) − 10. What is the mean level of this oscillatory motion?  -10 −10π 10 10π 10. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − ) + 1. What is the maximum speed ? 3 2  5 4 3 11. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − ) + 1. What is the minimum speed ? 3  -2 0 3 4 12. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − . What is the velocity of the particle at t ) + 1 3 3  2 1 = 6 1 4 13. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − nearest hundredth?  . What is the velocity of the particle at t ) + 1 3 1.08 2.01 2.08 1.01 5 = 12 to the https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 3/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 14. The velocity of a particle performing an oscillatory motion is given as π v(t) = 6 sin (2πt − . What is the amplitude of the particle? ) + 2 3 π 2 − 3 3  6 15. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − . What is the angular speed of the particle? ) + 1 3  π 4π 2π 3π 16. The velocity of a particle performing an oscillatory motion is given as π v(t) = 3 sin (2πt − . What is the inital phase constant? ) + 1 3 π π 4 3 π π 3 4 −  − 17. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I  = 5 cos ( 2πt 3 − π 2 . What is the amplitude of this sound? ) + 55 dB 5 dB 55 dB 50 dB 60 dB https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 4/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 18. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I 2πt = 5 cos ( π − 3 . What is the maximum intensity heard by ) + 55dB 2 him? 55 dB 45 dB 50 dB  60 dB 19. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I 2πt = 5 cos ( π − 3 . What is the minimum intensity heard by ) + 55dB 2 him?  55 dB 60 dB 50 dB 45 dB 20. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I π − 4πt = 3 cos ( π − 5 . What is the amplitude of the equation? ) + 35dB 3  dB 3 dB 3 4π 35 dB dB 5 21. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I  4πt = 3 cos ( π − 5 . What is the minimum intensity heard? ) + 35dB 3 38 dB 3 dB 32 dB 35 dB https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 5/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 22. The intensity of sound as heard by a person at a place where he is sitting is given by the equation I 2πt = 5 cos ( π − 3 . What is the magnitude of intensity he ) + 55dB 2 heard initially?  60 dB 45 dB 55 dB 50 dB 23. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the intensity of his affection when he meets his girl at t 1 = to the nearest hundredth? 10.99 2.99  2 14.99 15.99 24. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the intensity of his affection at t number?  15 9 12 14 = 4 to the nearest whole https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 6/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 25. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the intensity at t = 1 to the nearest hundredth? 15.98  16.89 14.98 13.89 26. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the maximum intensity of affection? 4  2 15 12 27. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the amplitude of his love affection? 15  20 10 5 28. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the period of his affection? 1 4π 4π  π 2 1 4 https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 7/8 11/12/23, 3:09 PM Solving a Word Problem Involving a Sine or Cosine Function in the Form f(x) = a\cos(bx+c) + d or f(x) = a\sin(bx+c)+d 29. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows π negative love. The intensity of his affection is modeled as L = 10 cos ( πt + ) + 5, 2 2 where t is in hours. What is the mean level of his affection? 15 10 20  5 30. The affection that a boy holds for his girl varies throughout the day. Sometimes he shows maximum love and care and sometimes he doubts her girl and thus shows negative love. The intensity of his affection is modeled as L πt = 10 cos ( π + 2 , ) + 5 2 where t is in hours. What is the phase constant of this affection model? π − 2  π 2 π π 3 6 https://study.com/skill/print/practice/solving-a-word-problem-involving-a-sine-or-cosine-function-in-the-form-f-x-a-cos-bx-plus-c-plus-d-or-f-x-a-sin-bx-pl… 8/8